Group #18069941 — subgroups

Subgroups — #18069941

Order 4864.

126 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14565390	C₂	1	1	yes	maximal, characteristic
2	#14561775	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1400	C₂	1	1	yes	maximal, characteristic
4	C₂×#10597269	C₄	1	1	yes	characteristic
5	C₂×C₈×Dic₁₉	C₄	1	1	yes	characteristic
6	#11926378	—	2	1	no	—
7	Dic₁₉⋊C₁₆	—	2	1	no	—
8	Dic₁₉⋊C₁₆	—	2	1	no	—
9	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
10	C₁₉×M₆₄	—	2	1	no	—
11	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×Dic₁₉	C₈	1	1	yes	characteristic
13	C₂²×C₁₉⋊C₈	C₈	1	1	yes	characteristic
14	C₁₉×M₃₂	—	4	1	no	—
15	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
17	C₈×Dic₁₉	—	2	1	no	—
18	C₈×Dic₁₉	—	2	1	no	—
19	#10597269	—	4	1	no	—
20	C₂×C₁₉⋊C₁₆	—	2	1	no	—
21	C₁₉×C₃₂	—	4	1	no	—
22	C₁₉⋊C₃₂	—	4	1	no	—
23	C₂²×C₄×C₁₉	C₂×C₈	1	1	yes	characteristic
24	C₂²×Dic₁₉	—	2	1	no	—
25	C₂×C₈×C₁₉	—	2	1	no	—
26	C₂×C₈×C₁₉	—	2	1	no	—
27	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₉	M₁₆	1	1	yes	characteristic
29	C₄×Dic₁₉	—	2	1	no	—
30	C₄×Dic₁₉	C₁₆	1	1	yes	characteristic
31	C₄×Dic₁₉	C₁₆	1	1	yes	characteristic
32	C₂×C₁₉⋊C₈	—	2	1	no	—
33	C₂×C₁₉⋊C₈	—	4	1	no	—
34	C₁₆×C₁₉	—	2	1	no	—
35	C₁₆×C₁₉	—	2	1	no	—
36	C₁₉⋊C₁₆	—	4	1	no	—
37	#7364	—	19	1	no	maximal, Sylow
38	C₂³×C₁₉	M₃₂	1	1	yes	characteristic
39	C₂×C₄×C₁₉	—	2	1	no	—
40	C₂×C₄×C₁₉	—	2	1	no	—
41	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
42	C₂×C₄×C₁₉	C₂×C₁₆	1	1	yes	characteristic
43	C₂×Dic₁₉	—	2	1	no	—
44	C₂×Dic₁₉	—	2	1	no	—
45	C₂×Dic₁₉	—	4	2	no	—
46	C₈×C₁₉	—	2	1	no	—
47	C₈×C₁₉	#99	1	1	yes	characteristic
48	C₈×C₁₉	#101	1	1	yes	characteristic
49	C₁₉⋊C₈	—	4	1	no	—
50	#2150	—	19	1	no	—
51	#1400	—	19	1	no	—
52	#1400	D₁₉	1	1	yes	characteristic
53	C₂²×C₁₉	—	2	1	no	—
54	C₂²×C₁₉	—	4	1	no	—
55	C₂²×C₁₉	C₂²⋊C₁₆	1	1	yes	characteristic
56	C₄×C₁₉	—	2	1	no	—
57	C₄×C₁₉	#324	1	1	yes	characteristic
58	C₄×C₁₉	#349	1	1	yes	characteristic
59	Dic₁₉	—	2	2	no	—
60	Dic₁₉	—	4	1	no	—
61	C₂×M₃₂	—	19	1	no	—
62	C₂×M₃₂	C₂×D₁₉	1	1	yes	characteristic
63	C₂×C₄×C₈	—	19	1	no	—
64	M₆₄	—	2	1	no	—
65	M₆₄	—	38	1	no	—
66	C₄⋊C₁₆	—	38	1	no	—
67	C₄⋊C₁₆	—	38	1	no	—
68	C₂×C₁₉	—	2	1	no	—
69	C₂×C₁₉	—	4	1	no	—
70	C₂×C₁₉	#1322	1	1	yes	characteristic
71	C₂²×C₈	—	19	1	no	—
72	C₂²×C₈	C₄×D₁₉	1	1	yes	characteristic
73	C₂×C₄²	—	19	1	no	—
74	M₃₂	—	4	1	no	—
75	M₃₂	—	76	1	no	—
76	C₂×C₁₆	—	38	1	no	—
77	C₂×C₁₆	D₇₆	1	1	yes	characteristic
78	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
79	C₄×C₈	—	38	1	no	—
80	C₄×C₈	—	38	1	no	—
81	C₃₂	—	4	1	no	—
82	C₃₂	—	76	1	no	—
83	C₁₉	#7364	1	1	yes	characteristic, complemented, Sylow
84	C₂²×C₄	—	38	1	no	—
85	C₂²×C₄	C₈×D₁₉	1	1	yes	characteristic
86	C₂×C₈	—	2	1	no	—
87	C₂×C₈	—	2	1	no	—
88	C₂×C₈	—	38	1	no	—
89	C₂×C₈	—	76	1	no	—
90	C₂×C₈	#64515	1	1	yes	characteristic
91	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
92	C₄²	—	19	1	no	—
93	C₄²	—	19	1	no	—
94	C₄²	—	38	1	no	—
95	C₁₆	—	2	1	no	—
96	C₁₆	—	2	1	no	—
97	C₁₆	—	76	1	no	—
98	C₂³	#10597255	1	1	yes	characteristic
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	38	1	no	—
102	C₂×C₄	—	38	1	no	—
103	C₂×C₄	—	76	2	no	—
104	C₂×C₄	C₁₆×D₁₉	1	1	yes	characteristic
105	C₂×C₄	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
106	C₈	—	2	1	no	—
107	C₈	—	76	1	no	—
108	C₈	#10597263	1	1	yes	characteristic
109	C₈	#10597281	1	1	yes	characteristic
110	C₂²	—	2	1	no	—
111	C₂²	—	4	1	no	—
112	C₂²	(C₂×D₁₉)⋊C₁₆	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	38	2	no	—
115	C₄	—	76	1	no	—
116	C₄	#11926269	1	1	yes	characteristic
117	C₄	#11926325	1	1	yes	characteristic
118	C₂	—	2	1	no	—
119	C₂	—	4	1	no	—
120	C₂	#14561574	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565390

C₂

yes

maximal, characteristic

#14561775

C₂

yes

maximal, characteristic

C₁₉×#1400

C₂

yes

maximal, characteristic

C₂×#10597269

C₄

yes

characteristic

C₂×C₈×Dic₁₉

C₄

yes

characteristic

#11926378

—

Dic₁₉⋊C₁₆

—

Dic₁₉⋊C₁₆

—

C₂×C₁₉×M₃₂

C₂²

yes

characteristic

C₁₉×M₆₄

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₉

C₈

yes

characteristic

C₂²×C₁₉⋊C₈

C₈

yes

characteristic

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₈×Dic₁₉

—

C₈×Dic₁₉

—

#10597269

—

C₂×C₁₉⋊C₁₆

—

C₁₉×C₃₂

—

C₁₉⋊C₃₂

—

C₂²×C₄×C₁₉

C₂×C₈

yes

characteristic

C₂²×Dic₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

M₁₆

yes

characteristic

C₄×Dic₁₉

—

C₄×Dic₁₉

C₁₆

yes

characteristic

C₄×Dic₁₉

C₁₆

yes

characteristic

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₉⋊C₁₆

—

#7364

—

maximal, Sylow

C₂³×C₁₉

M₃₂

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

C₂×C₁₆

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

yes

C₈×C₁₉

yes

C₁₉⋊C₈

—

#2150

—

#1400

—

#1400

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²⋊C₁₆

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

Dic₁₉

—

C₂×M₃₂

—

C₂×M₃₂

C₂×D₁₉

yes

characteristic

C₂×C₄×C₈

—

M₆₄

—

M₆₄

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1322

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₄×D₁₉

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

D₇₆

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₃₂

—

C₃₂

—

C₁₉

#7364

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₈×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#64515

yes

characteristic

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

C₄²

—

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

C₂³

#10597255

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₁₆×D₁₉

yes

characteristic

105

C₂×C₄

(C₂×D₁₉)⋊C₈

yes

characteristic

106

C₈

—

107

C₈

—

108

C₈

#10597263

yes

characteristic

109

C₈

#10597281

yes

characteristic

110

C₂²

—

111

C₂²

—

112

C₂²

(C₂×D₁₉)⋊C₁₆

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

#11926269

yes

characteristic

117

C₄

#11926325

yes

characteristic

118

C₂

—

119

C₂

—

120

C₂

#14561574

yes

characteristic

	subgroup	G/H
center	C₈	#10597263
commutator	C₂×C₄×C₁₉	C₂×C₁₆
Frattini	C₂×M₃₂	C₂×D₁₉
Fitting	C₁₉×#1400	C₂
socle	C₂×C₁₉	#1322
prime radical	C₂³×C₁₉	M₃₂
cosocle	C₂×C₁₉×M₃₂	C₂²
hypercenter	#1400	D₁₉
hypocenter	C₁₉	#7364
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×M₃₂ ◁ #1400

subgroup

G/H

center

C₈

#10597263

commutator

C₂×C₄×C₁₉

C₂×C₁₆

Frattini

C₂×M₃₂

C₂×D₁₉

Fitting

C₁₉×#1400

C₂

socle

C₂×C₁₉

#1322

prime radical

C₂³×C₁₉

M₃₂

cosocle

C₂×C₁₉×M₃₂

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×M₃₂ ◁ #1400

N	H ≅ G/N	type
83. C₁₉	#7364	semidirect

H ≅ G/N

type

83. C₁₉

#7364

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14565390	2
#14561775	2
C₁₉×#1400	2
#7364	19

subgroup

index

#14565390

#14561775

C₁₉×#1400

#7364

Subgroups — #18069941

Conjugacy classes of subgroups

Complements

Maximal subgroups